Statistics assignment help
| The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience. |
| Admissions | Probability |
| 1,060 | 0.6 |
| 1,400 | 0.1 |
| 1,620 | 0.3 |
|
|
| 1. | What is the expected number of admissions for the fall semester? |
| Expected number of admissions |
| 2. | Compute the variance and the standard deviation of the number of admissions. (Round your standard deviation to 2 decimal places.) |
| Variance | |
| Standard deviation | |
|
|
|
| The Internal Revenue Service is studying the category of charitable contributions. A sample of 32 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 32 returns, 7 had charitable contributions of more than $1,000. Suppose 6 of these returns are selected for a comprehensive audit. |
| a | You should use the hypergeometric distribution is appropriate. Because |
| b. | What is the probability exactly one of the six audited had a charitable deduction of more than $1,000?(Round your answer to 4 decimal places.) |
| Probability |
| c. | What is the probability at least one of the audited returns had a charitable contribution of more than $1,000? (Round your answer to 4 decimal places.) |
| Probability |
| According to the “January theory,” if the stock market is up for the month of January, it will be up for the year. If it is down in January, it will be down for the year. According to an article in The Wall Street Journal, this theory held for 25 out of the last 34 years. Suppose there is no truth to this theory; that is, the probability it is either up or down is 0.5. |
| What is the probability this could occur by chance? (Round your answer to 6 decimal places.) |
| Probability |
| Customers experiencing technical difficulty with their internet cable hookup may call an 800 number for technical support. It takes the technician between 90 seconds and 14 minutes to resolve the problem. The distribution of this support time follows the uniform distribution. |
| a. | What are the values for a and b in minutes? (Do not round your intermediate calculations. Round your answers to 1 decimal place.) |
| a | |
| b | |
| b-1. | What is the mean time to resolve the problem? (Do not round your intermediate calculations. Round your answer to 2 decimal places.) |
| Mean |
| b-2. | What is the standard deviation of the time? (Do not round your intermediate calculations. Round your answer to 2 decimal places.) |
| Standard deviation |
| c. | What percent of the problems take more than 5 minutes to resolve? (Do not round your intermediate calculations. Round your answer to 2 decimal places.) |
| Percent | % |
| d. | Suppose we wish to find the middle 50% of the problem-solving times. What are the end points of these two times? (Do not round your intermediate calculations. Round your answers to 3 decimal places.) |
| End point 1 | |
| End point 2 | |
| A normal population has a mean of 20 and a standard deviation of 4. |
| a. | Compute the z value associated with 24. (Round your answer to 2 decimal places.) |
| Z |
| b. | What proportion of the population is between 20 and 24? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) |
| Proportion |
| c. | What proportion of the population is less than 15? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) |
| Proportion |
| Assume that the hourly cost to operate a commercial airplane follows the normal distribution with a mean of $5,500 per hour and a standard deviation of $394. |
| What is the operating cost for the lowest 4% of the airplanes? (Round z value to 2 decimal places and round final answer to nearest whole dollar.) |
| Operating cost | $ |
| The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,400. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 620 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last. |
| How many pages should the manufacturer advertise for each cartridge if it wants to be correct 95 percent of the time? (Round z value to 2 decimal places. Round your answer to the nearest whole number.) |
| Pages |
| A study of long-distance phone calls made from General Electric Corporate Headquarters in Fairfield, Connecticut, revealed the length of the calls, in minutes, follows the normal probability distribution. The mean length of time per call was 4.40 minutes and the standard deviation was 0.50 minutes. |
| a. | What fraction of the calls last between 4.40 and 5.20 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) |
| Fraction of calls |
| b. | What fraction of the calls last more than 5.20 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) |
| Fraction of calls |
| c. | What fraction of the calls last between 5.20 and 6.00 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) |
| Fraction of calls |
| d. | What fraction of the calls last between 4.00 and 6.00 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) |
| Fraction of calls |
| e. | As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 4 percent of the calls. What is this time? (Round z-score computation to 2 decimal places and your final answer to 2 decimal places.) |
| Duration |
| a. | List all samples of size 3, and compute the mean of each sample. (Round your mean value to 2 decimal places.) |
| Sample | Values | Sum | Mean |
| 1 | |||
| 2 | |||
| 3 | |||
| 4 | |||
| 5 | |||
| 6 | |||
| 7 | |||
| 8 | |||
| 9 | |||
| 10 | |||
| b. | Compute the mean of the distribution of sample means and the population mean. (Round your answers to 2 decimal places.) |
| Sample means | |
| Population mean | |
| The mean age at which men in the United States marry for the first time follows the normal distribution with a mean of 24.8 years. The standard deviation of the distribution is 2.7 years. |
| For a random sample of 63 men, what is the likelihood that the age at which they were married for the first time is less than 25 years? (Round z value to 2 decimal places. Round your answer to 4 decimal places.) |
| Probability |
rev: 04_04_2016_QC_CS-47404
Which of the following is an example of a continuous variable?
Tons of concrete to complete a parking garage
Number of students in a statistics class
Zip codes of shoppers
Rankings of baseball teams in a league
The incomes of 50 loan applicants are obtained. Which level of measurement is income?
Nominal
Ordinal
Interval
Ratio
The members of each basketball team wear numbers on their jerseys. What scale of measurement are these numbers considered?
Nominal
Ordinal
Interval
Ratio
The reported unemployment is 5.5% of the population. What measurement scale is used to measure unemployment?
Nominal
Ordinal
Interval or ratio
Descriptive
The Nielsen Ratings break down the number of people watching a particular television show by age. What level of measurement is age?
Nominal
Ordinal
Interval
Ratio
An example of a qualitative variable is _________________.
Number of children in a family
Weight of a person
Color of ink in a pen
Miles between oil changes
| Two thousand six hundred frequent business travelers are asked which midwestern city they prefer: Indianapolis, Saint Louis, Chicago, or Milwaukee. 113 liked Indianapolis best, 455 liked Saint Louis, 1395 liked Chicago, and the remainder preferred Milwaukee. Develop a frequency table and a relative frequency table to summarize this information. (Round relative frequency to 3 decimal places.) |
| City | Frequency | Relative Frequency |
| Indianapolis | ||
| St. Louis | ||
| Chicago | ||
| Milwaukee | ||
| The Cambridge Power and Light Company selected a random sample of 20 residential customers. Following are the amounts, to the nearest dollar, the customers were charged for electrical service last month: | ||
| 53 | 47 | 53 | 50 | 23 | 46 | 75 | 45 | 62 | 76 |
| 67 | 61 | 37 | 34 | 53 | 62 | 36 | 66 | 63 | 61 |
| a. | Compute the arithmetic mean.(Round your answer to 2 decimal places.) |
| The mean is | $ |
| b. | Indicate whether it is a statistic or a parameter. |
| This is a . |
Statistic or paremeter
| Consider these five values a population: 6, 4, 5, 4, and 7. |
| a. | Determine the mean of the population. (Round your answer to 1 decimal place.) |
| Arithmetic mean |
| b. | Determine the variance of the population. (Round your answer to 2 decimal places.) |
| Variance |
| An investor buys 100 shares of AT&T stock and records its price change daily. Which concept of probability would you use to estimate the probability of an individual event? |
| Probability of an individual event |
Empirical
Classical
| A sample of 33 observations is selected from a normal population. The sample mean is 30, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.05 significance level. |
| H0 : μ ≤ 29 |
| H1 : μ > 29 |
| a. | Is this a one- or two-tailed test? | ||||
|
| b. | What is the decision rule? (Round your answer to 3 decimal places.) |
| H0, when z > |
| c. | What is the value of the test statistic? (Round your answer to 2 decimal places.) |
| Value of the test statistic |
| d. | What is your decision regarding H0? | ||||
|
| There is evidence to conclude that the population mean is greater than 29. |
| e. | What is the p-value? (Round your answer to 4 decimal places.) |
| p-value | |
| At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $74 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $4.04. Over the first 36 days she was employed at the restaurant, the mean daily amount of her tips was $75.04. At the 0.02 significance level, can Ms. Brigden conclude that her daily tips average more than $74? |
| a. | State the null hypothesis and the alternate hypothesis. | ||||||||
|
| b. | State the decision rule. | ||||||||
|
| c. | Compute the value of the test statistic. (Round your answer to 2 decimal places.) |
| Value of the test statistic |
| d. | What is your decision regarding H0? | ||||
|
| e. | What is the p-value? (Round your answer to 4 decimal places.) |
| p-value |
| The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 37 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 41 sales representatives reveals that the mean number of calls made last week was 40. The standard deviation of the sample is 5.6 calls. Using the 0.025 significance level, can we conclude that the mean number of calls per salesperson per week is more than 37? |
| H0 : μ ≤ 37 |
| H1 : μ > 37 |
| 1. | Compute the value of the test statistic. (Round your answer to 3 decimal places.) |
| Value of the test statistic |
| 2. | What is your decision regarding H0? |
| H0. The mean number of calls is than 37 per week. |
| A United Nations report shows the mean family income for Mexican migrants to the United States is $28,540 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 26 Mexican family units reveals a mean to be $30,500 with a sample standard deviation of $10,500. Does this information disagree with the United Nations report? Apply the 0.01 significance level. |
| a. | State the null hypothesis and the alternate hypothesis. |
| H0: μ = | |
| H1: μ ≠ | |
| b. | State the decision rule for .01 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) |
| Reject H0 if t is not between and |
| c. | Compute the value of the test statistic. (Round your answer to 2 decimal places.) |
| Value of the test statistic |
| d. | Does this information disagree with the United Nations report? Apply the 0.01 significance level. |
| . This data the report. |
| The following information is available. |
| H0 : μ ≥ 220 |
| H1 : μ < 220 |
| A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level. |
| a. | Is this a one- or two-tailed test? | ||||
|
| b. | What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) |
| H0 when z < |
| c. | What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) |
| Value of the test statistic |
| d. | What is your decision regarding H0? | ||||
|
| e. | What is the p-value? (Round your answer to 4 decimal places.) |
| p-value |
| Given the following hypotheses: |
| H0 : μ ≤ 10 |
| H1 : μ > 10 |
| A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation 3. Using the .05 significance level: |
| a. | State the decision rule. (Round your answer to 3 decimal places.) |
| Reject H0 if t > |
| b. | Compute the value of the test statistic. (Round your answer to 3 decimal places.) |
| Value of the test statistic |
| c. | What is your decision regarding the null hypothesis? |
| H0. There is evidence to conclude that the population mean is greater than 10. |
| Given the following hypotheses: |
| H0 : μ = 400 |
| H1 : μ ≠ 400 |
| A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level: |
| a. | State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.) |
| Reject H0 when the test statistic is the interval (, ). |
| b. | Compute the value of the test statistic. (Round your answer to 3 decimal places.) |
| Value of the test statistic |
| c. | What is your decision regarding the null hypothesis? | ||||
|
| The production department of Celltronics International wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, 3 employees were assigned to assemble the subassemblies. They produced 8 during a one-hour period. Then 5 employees assembled them. They produced 13 during a one-hour period. The complete set of paired observations follows. |
| Number of Assemblers | One-Hour Production (units) |
| 3 | 8 |
| 5 | 13 |
| 2 | 5 |
| 6 | 23 |
| 4 | 16 |
| The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees. |
Click here for the Excel Data File
| b. | A scatter diagram is provided below. Based on it, does there appear to be any relationship between the number of assemblers and production? |
| |
|
| , as the number of assemblers , so does the production. |
| c. | Compute the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round sx, sy and r to 3 decimal places.) |
| X | Y | ( |
( |
( |
||
| 3 | 8 | -5 | 25 | |||
| 5 | 13 | 1 | 1 | 0 | ||
| 2 | 5 | -8 | 64 | |||
| 6 | 23 | 2 | 4 | 20 | ||
| 4 | 16 | 3 | 0 | 0 | ||
| = | = | sx | = |
| sy | = | r | = |
| The following sample observations were randomly selected. (Round your answers to 2 decimal places.) |
| X: | 4 | 5 | 3 | 6 | 10 |
| Y: | 8.8 | 10.6 | 7 | 15.4 | 18.6 |
| a. | The regression equation is = + X |
| b. | When X is 8 this gives = |
| Bi-lo Appliance Super-Store has outlets in several large metropolitan areas in New England. The general sales manager aired a commercial for a digital camera on selected local TV stations prior to a sale starting on Saturday and ending Sunday. She obtained the information for Saturday–Sunday digital camera sales at the various outlets and paired it with the number of times the advertisement was shown on the local TV stations. The purpose is to find whether there is any relationship between the number of times the advertisement was aired and digital camera sales. The pairings are: |
| Location of | Number of | Saturday–Sunday Sales |
| TV Station | Airings | ($ thousands) |
| Providence | 4 | 15 |
| Springfield | 2 | 8 |
| New Haven | 5 | 21 |
| Boston | 6 | 24 |
| Hartford | 3 | 17 |
| a. | What is the dependent variable? |
| is the dependent variable. |
| c. | Determine the correlation coefficient. (Round your answer to 2 decimal places.) |
| Coefficient of correlation |
| d. | Interpret these statistical measures. |
| The statistical measures obtained here indicate correlation between the variables. |
| The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year. |
| Car | Age (years) | Selling Price ($000) | Car | Age (years) | Selling Price ($000) |
| 1 | 9 | 8.1 | 7 | 8 | 7.6 |
| 2 | 7 | 6.0 | 8 | 11 | 8.0 |
| 3 | 11 | 3.6 | 9 | 10 | 8.0 |
| 4 | 12 | 4.0 | 10 | 12 | 6.0 |
| 5 | 8 | 5.0 | 11 | 6 | 8.6 |
| 6 | 7 | 10.0 | 12 | 6 | 8.0 |
Click here for the Excel Data File
| a. | If we want to estimate selling price on the basis of the age of the car, which variable is the dependent variable and which is the independent variable? |
| is the independent variable and is the dependent variable. |
| b-1. | Determine the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) |
| X | Y | ( |
( |
( |
||
| 9.0 | 8.1 | 1.192 | 0.007 | 1.420 | 0.099 | |
| 7.0 | 6.0 | -0.908 | 3.674 | 0.825 | 1.741 | |
| 11.0 | 3.6 | 2.083 | 4.340 | 10.945 | -6.892 | |
| 12.0 | 4.0 | 3.083 | 9.507 | 8.458 | -8.967 | |
| 8.0 | 5.0 | -0.917 | -1.908 | 3.642 | 1.749 | |
| 7.0 | 10.0 | -1.917 | 3.092 | 9.558 | -5.926 | |
| 8.0 | 7.6 | -0.917 | 0.692 | 0.840 | -0.634 | |
| 11.0 | 8.0 | 2.083 | 1.092 | 4.340 | 2.274 | |
| 10.0 | 8.0 | 1.083 | 1.092 | 1.174 | 1.192 | |
| 12.0 | 6.0 | 3.083 | -0.908 | 9.507 | 0.825 | |
| 6.0 | 8.6 | -2.917 | 1.692 | 8.507 | 2.862 | -4.934 |
| 6.0 | 8.0 | -2.917 | 1.092 | 8.507 | 1.192 | -3.184 |
| 107.000 | 82.900 | |||||
| = | = | sx | = | sy | = |
| r | = |
| b-2. | Determine the coefficient of determination. (Round your answer to 3 decimal places.) |
| c. | Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative?(Round your answer to nearest whole number.) |
| correlation between age of car and selling price. So, % of the variation in the selling price is explained by the variation in the age of the car. |
| Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 20 stations last Tuesday, the correlation was .78. |
| At the .01 significance level, is the correlation in the population greater than zero? (Round your answer to 3 decimal places.) |
| The test statistic is . |
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